Circuit Theorems 1
Introduction Linearity property Superposition Source transformations Thevenin’s theorem Norton’s theorem Maximum power transfer Circuit Theorems2
Thevenin’s Theorem Thevenin’s Theorem Thevenin’s theorem states that a linear two- terminal circuit can be replaced by an equivalent circuit consisting of a voltage source V Th in series with a resistor R Th where V Th is the open circuit voltage at the terminals and R Th is the input or equivalent resistance at the terminals when the independent source are turn off. Circuit Theorems3
Property of Linear Circuits Circuit Theorems4 i v v i Any two-terminal Linear Circuits + - V th I sc Slope=1/R th
Circuit Theorems5
How to Find Thevenin’s Voltage Equivalent circuit: same voltage-current relation at the terminals. Open circuit voltage at a-b Circuit Theorems6
How to Find Thevenin’s Resistance Circuit Theorems7
CASE 1 If the network has no dependent sources: ●Turn off all independent source. ●R TH : can be obtained via simplification of either parallel or series connection seen from a-b Circuit Theorems8
CASE 2 If the network has dependent sources ●Turn off all independent sources. ●Apply a voltage source v o at a-b ●Alternatively, apply a current source i o at a-b Circuit Theorems9
The Thevenin’s resistance may be negative, indicating that the circuit has ability providing power Circuit Theorems10
Simplified circuit Voltage divider Circuit Theorems11
Example 8 Find the Thevenin’s equivalent circuit of the circuit shown, to the left of the terminals a-b. Then find the current through R L for R L = 6, 16, and 36 . Circuit Theorems12
Find R th Circuit Theorems13
Find V th Circuit Theorems14
Norton’s Theorem Norton’s theorem states that a linear two-terminal circuit can be replaced by equivalent circuit consisting of a current source I N in parallel with a resistor R N where I N is the short-circuit current through the terminals and R N is the input or equivalent resistance at the terminals when the independent source are turn off. Circuit Theorems15
Circuit Theorems16 v i V th -I N Slope=1/R N
How to Find Norton Current Thevenin and Norton resistances are equal: Short circuit current from a to b : Circuit Theorems17
Thevenin or Norton equivalent circuit : The open circuit voltage v oc across terminals a and b The short circuit current i sc at terminals a and b The equivalent or input resistance R in at terminals a and b when all independent source are turn off. Circuit Theorems18
Example 11 Find the Norton equivalent circuit of the circuit shown. Circuit Theorems19
Example 11 Circuit Theorems20
Example 11 Circuit Theorems21
Example 11 Circuit Theorems22
Example 11 Circuit Theorems23
Maximum Power Transfer Circuit Theorems24
Maximum power is transferred to the load when the load resistance equals the Thevenin resistance as seen the load (R L = R TH ). Circuit Theorems25
Circuit Theorems26
Example 13 Find the value of R L for maximum power transfer in the circuit shown. Find the maximum power. Circuit Theorems27
Example 13 Circuit Theorems28
Example 13 Circuit Theorems29
Summary Circuit Theorems30